Osama bin Laden was considering changing al-Qaida's name to improve its image among Muslims, according to documents obtained by US special forces from the compound where he was killed.

A letter apparently written in the months before he died indicates that Bin Laden felt al-Qaida, which means "the base", was not sufficiently religious and did not reinforce the message that the group considered itself to be engaged in a holy war against the enemies of Islam.

A name change would allow al-Qaida to distance itself from growing criticism within the Islamic world that it was responsible for killing large numbers of Muslims, Bin Laden wrote.

The letter, described to the Associated Press news agency by US officials, provides further evidence that Bin Laden was considering increasingly desperate measures to retain support for his campaign of violence and to maintain the relevance of his group.

However, Bin Laden may have been helped in Pakistan by members of a separate local militant group that has close connections to the Pakistani security establishment. The New York Times reported that records of the mobile phone belonging to the courier who helped conceal Bin Laden – and eventually inadvertently led the CIA to him – revealed frequent calls to the Harkat-ul-Mujahideen (HUM) group.

Founded in the 1980s, HUM sent members to fight in Afghanistan alongside the Taliban and against Indian security forces in the disputed Himalayan territory of Kashmir in the 1990s.

Since 2001 the group has survived successive crackdowns announced by Pakistani authorities. It retains close ties to Pakistani security services.

The question of the name of the group led by Bin Laden has often posed problems. Minutes of the meeting at which it was founded in 1988 reveal that "al-Qaida" was chosen in some haste.

One suggestion has been that the name referred to a database of contact details for international militants who had fought in Afghanistan against Soviet occupiers. Another is that it refers to the "al-Qaida al-Sulbah" or vanguard of the strong, which militant ideologues were calling for at the time to continue the extremist campaign beyond south-west Asia.

One former militant on trial in the US referred to al-Qaida (which in Arabic can also mean a maxim or method), as "a formula system", denying that it was the name of a group.

When Ayman al-Zawahiri, Bin Laden's then deputy and now successor, formally fused his own group Egyptian Islamic Jihad with al-Qaida the full name of the group was "al-Qaida al-Jihad" or "the base for the jihad".

In the leaked letter Bin Laden is reported to have complained that the last part was often omitted. This, he wrote, allowed the west to "claim deceptively that they are not at war with Islam". Instead, the letter reveals, Bin Laden pondered alternatives including Taifat al-Tawheed Wal-Jihad (Monotheism and Jihad Group), or Jama'at I'Adat al-Khilafat al-Rashida (Restoration of the Caliphate Group).

On Wednesday Barack Obama, in his speech to the nation on withdrawing troops from Afghanistan, said that information recovered from Bin Laden's compound showed that al-Qaida was "under enormous strain".

"Bin Laden expressed concern that al-Qaida had been unable to effectively replace senior terrorists that had been killed and that al-Qaida has failed in its effort to portray America as a nation at war with Islam, thereby draining more widespread support," Obama said.

The recipient of the letter has not been identified. US investigators believe that Bin Laden only communicated with his most senior commanders, including Zawahiri and Mustafa Abu al-Yazid, a senior militant who ran external operations for the group as well as fundraising and liason with the Afghan Taliban. Al-Yazid was killed in a US air strike last year. Because of the courier system used by Bin Laden it is unclear to US intelligence whether the letter was actually sent.

In one letter sent to Zawahiri within the past year or so, Bin Laden said al-Qaida's image was suffering because of attacks that had killed Muslims, particularly in Iraq, officials said.

Bin Laden also wrote that he found the suggestion of one militant in Yemen that blades be attached to a tractor or other farm machine to create a "killing machine" in the US "unacceptable". Al-Qaida was not about "indiscriminate killing", he said. Bin Laden and his senior associates have long struggled to make sure the disparate elements of the group and its various affiliated networks only attack targets they consider as legitimate.

A series of letters and envoys were sent to Iraq in a bid to moderate – or at least better focus – the brutality of international extremists there. In a question and answer internet session four years ago, Zawahiri was bombarded by aggressive demands that he justify the number of deaths of Muslims resulting from al-Qaida attacks.

Successive polls in the Muslim world have shown decreasing support for radical Islam and Bin Laden since around 2005. Yesterday in Jeddah, Saudi Arabia, where Bin Laden was born, few expressed any support for the dead extremist.

"He was a freedom fighter against the Russians but then took the wrong path. Violence like that is never justified whatever the provocation," said Abdulillah, a 42-year-old shopkeeper. In other journal entries and letters, US officials said, Bin Laden wrote that he was frustrated many of his trusted longtime comrades, whom he had fought alongside in Afghanistan, had been killed or captured. Using his courier system Bin Laden could still exercise an element of operational control over al-Qaida, but increasingly the men he was directing were younger and inexperienced, the fugitive leader complained.

With the senior militants who had vouched for new recruits dead or in prison, Bin Laden, confined to his walled compound and cut off from the phone or internet for security reasons, was without any means of verifying new recruits' competence or loyalty, he wrote. The US has now essentially completed the review of documents taken from Bin Laden's compound, though intelligence analysts will continue to mine the data for a long time, officials have said.